Bayesian Estimation Based on Progressively Type-II Censored Samples from Compound Rayleigh Distribution

Abstract

This paper considers inference under progressive type-II censoring scheme with a compound Rayleigh failure time distribution. The maximum likelihood (ML) and the Bayes estimators for the two unknown parameters of the compound Rayleigh distribution (CRD) distribution are derived. A Bayesian approach using Markov chain Monte Carlo (MCMC) method to generate from the posterior distributions and in turn computing the Bayes estimators are developed. Point estimation and confidence intervals based on maximum likelihood and bootstrap methods are also proposed. The approximate Bayes estimators have been obtained under the assumptions of informative and non-informative priors. An example with the real data is discussed to illustrate the proposed methods. Finally, we made comparisons between the maximum likelihood and different Bayes estimators using a Monte Carlo simulation study.

Keywords

• Compound Rayleigh distribution (CRD); Progressive type-II censoring; Bootstrap methods; Bayesian and non-Bayesian approach; Markov chain Monte Carlo (MCMC); Gibbs and Metropolis sampler